We have developed an approach for performing ABC in a topological context that is able to derive posterior distributions over model parameters that can accurately reproduce multiple different classes of behaviour and structure observed within the data.
We applied extended persistence, which strictly quantifies more topological features than ordinary persistence. Other topological shape statistics have focussed on sweeping across data in multiple different directions [1]}, [2]}, [3]}; their utility for parameter inference and model selection will be explored in future studies.
